CATEGORICAL JUDGMENTS AND PROPOSITIONS 253 



not merely with the internal consistency of our concepts and 

 judgments, but with their truth (10, 17, 54), not merely with 

 what may be but with what is, it should certainly take account 

 of the whole general question whether or how far the objects, 

 of which we think and judge, are supposed by us to be not 

 merely possible but actual^ and whether such a supposition even 

 enters into our judgments as a part of their very meaning. Even 

 from the narrower point of view of formal logic, the propriety of 

 dealing with the question is thus defended by Dr. Keynes : J &quot;It 

 is, of course, no function of logic to determine whether or not cer 

 tain classes actually exist in any given universe of discourse, any 

 more than it is the function of logic to determine whether given 

 propositions are true or false. But it does not follow that logic 

 has therefore no concern with any questions relating to objective 

 existence. For, just as certain propositions being given true, 

 logic determines what other propositions will as a consequence 

 also be true ; so given an assertion or a set of assertions to the 

 effect that certain combinations do or do not exist in a given uni 

 verse of discourse, it can determine what other assertions about 

 existence in the same universe of discourse follow therefrom.&quot; 



Nor can it be contended that the traditional Aristotelean 

 logic always treated the import and implications of our judgments 

 without making any suppositions as to the existence, in any 

 actual sphere, of the objects compared in those judgments : that 

 it merely supposed these objects to exist in the sphere of possible 

 or thinkable things, without inquiring into their actual existence. 

 For, without indeed raising this latter question explicitly, it made 

 certain tacit assumptions by the very fact that it accepted the 

 opposites and eductions given in Chaps. V. and VI. as valid un 

 conditionally and without qualification. 



For instance, the process of converting an A or an I proposition does 

 not seem to be valid unless the existence of 5 in the universe of discourse is 

 either taken as implied by the A or I proposition, or assumed as an independent 

 datum. The propositions &quot; All S s are P s &quot; and &quot; Some S s are P s &quot; imply 

 at all events that if there are any S s there must be some P s in the sphere 

 referred to. But they do not seem necessarily to imply that if there are P s 

 there are S s. If, however, we convert them to &quot; Some P s are S s &quot; we have 

 in this converse the implication that if there are P s there are S s in the 

 sphere referred to : i.e. in the conversion of an A or an I proposition we have in 



of the Deity. But does this concept represent the reality aright ? Proof based on 

 the actual facts of our experience will alone determine this. 

 1 op. cit., p. 215. 



